Finite Group Databasebeta

← C22×#13093955 #20251959

Subgroups — C22×#13093955 #20251959

Order 6016.

600 conjugacy classes of subgroups; only the 349 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 349 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C47⋊C8C211yesmaximal, characteristic
2C22×C4⋊Dic47C211yesmaximal, characteristic
3C2×#13093955C2112yesmaximal, direct product factor
4C22×C4⋊C4×C47C211yesmaximal, characteristic
5C23×Dic47—21no—
6C22×C47⋊C8C418yescomplemented
7C22×C47⋊C8C2216yes—
8C2×C4⋊Dic47—23no—
9C2×C4⋊Dic47C2216yes—
10#13093955C22116yesdirect product factor
11C23×C4×C47—21no—
12C23×C4×C47C2211yescharacteristic
13C2×C4⋊C4×C47—23no—
14C2×C4⋊C4×C47C2216yes—
15C24×C47D411yescharacteristic
16C22×C4×C47—26no—
17C22×C4×C47—44no—
18C22×C4×C47C2×C414yes—
19C22×C4×C47D413yes—
20C22×C4×C47Q814yes—
21C22×C4×C47C2313yes—
22C22×Dic47—26no—
23C22×Dic47—44no—
24C4⋊C4×C47—26no—
25C4⋊C4×C47C2314yes—
26C4⋊Dic47—26no—
27C4⋊Dic47C2314yes—
28C2×C47⋊C8C2×C4124yescomplemented
29C2×C47⋊C8C2314yes—
30C23×C47C4⋊C414yes—
31C23×C47SD1614yes—
32C23×C47SD1614yes—
33C23×C47C2×D413yes—
34C2×C4×C47—24no—
35C2×C4×C47—412no—
36C2×C4×C47C4⋊C4112yes—
37C2×C4×C47C22×C416yes—
38C2×C4×C47C2×D413yes—
39C2×C4×C47C2×Q816yes—
40C2×C4×C47C2411yescharacteristic
41C2×Dic47—24no—
42C2×Dic47—412no—
43C47⋊C8C22×C418yescomplemented
44C22×C47#106116yescomplemented
45C22×C47C2×C4⋊C416yes—
46C22×C47C2×SD1616yes—
47C22×C47C2×SD1616yes—
48C22×C47C22×D411yescharacteristic
49C4×C47—44no—
50C4×C47C2×C4⋊C416yes—
51C4×C47C23×C411yescharacteristic
52C4×C47C22×Q811yescharacteristic
53Dic47—44no—
54C22×#106—471nomaximal, Sylow
55C2×C47C2×#106112yescomplemented
56C2×C47C22×C4⋊C411yescharacteristic
57C2×C47C22×SD1611yescharacteristic
58C2×C47C22×SD1611yescharacteristic
59C23×C8—471no—
60C22×C4⋊C4—471no—
61C22×C4⋊C4D4711yescharacteristic
62C2×#106—4712no—
63C47C22×#10611yescharacteristic, complemented, Sylow
64C23×C4—21no—
65C23×C4—941no—
66C23×C4C2×D4711yescharacteristic
67C22×C8—478no—
68C22×C8—476no—
69C2×C4⋊C4—23no—
70C2×C4⋊C4—476no—
71C2×C4⋊C4—943no—
72C2×C4⋊C4C2×D4716yes—
73#106—4716no—
74C24C22⋊D4711yescharacteristic
75C22×C4—26no—
76C22×C4—44no—
77C22×C4—946no—
78C22×C4—1884no—
79C22×C4Dic9414yes—
80C22×C4C4×D4714yes—
81C22×C4C22⋊D4713yes—
82C22×C4C22×D4713yes—
83C2×C8—4724no—
84C2×C8—474no—
85C4⋊C4—26no—
86C4⋊C4—474no—
87C4⋊C4—946no—
88C4⋊C4C22×D4714yes—
89C23Dic47⋊C414yes—
90C23#1062533514yes—
91C23#1062533614yes—
92C23C2×C22⋊D4713yes—
93C2×C4—24no—
94C2×C4—412no—
95C2×C4—944no—
96C2×C4—18812no—
97C2×C4Dic47⋊C4112yes—
98C2×C4C2×Dic9416yes—
99C2×C4C2×C4×D4716yes—
100C2×C4C2×C22⋊D4713yes—
101C2×C4C23×D4711yescharacteristic
102C8—478no—
103C22#13093955116yesdirect product factor
104C22C2×Dic47⋊C416yes—
105C22C2×#1062533616yes—
106C22C2×#1062533516yes—
107C22C22×C22⋊D4711yescharacteristic
108C4—44no—
109C4—1884no—
110C4C2×Dic47⋊C416yes—
111C4C22×C4×D4711yescharacteristic
112C4C22×Dic9411yescharacteristic
113C2C2×#13093955112yesdirect product factor
114C2C22×Dic47⋊C411yescharacteristic
115C2C22×#1062533611yescharacteristic
116C2C22×#1062533511yescharacteristic
subgroupG/H
centerC24C22⋊D47
commutatorC4×C47C23×C4
FrattiniC2×C4C23×D47
FittingC22×C4⋊C4×C47C2
socleC24×C47D4
hypercenterC22×C4⋊C4D47
hypocenterC47C22×#106
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
3. C2×#13093955C2direct (N × H)
6. C22×C47⋊C8C4semidirect
10. #13093955C22direct (N × H)
28. C2×C47⋊C8C2×C4semidirect
43. C47⋊C8C22×C4semidirect
44. C22×C47#106semidirect
55. C2×C47C2×#106semidirect
63. C47C22×#106semidirect
103. C22#13093955direct (N × H)
113. C2C2×#13093955direct (N × H)